The Particle Time Derivative of the Characteristic Geometric Quantities on Soft Curved Surface in Lagrangian Description
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Abstract
This paper studies the particle time derivatives of the characteristic geometric quantities on soft curved surfaces in Lagrangian description. On the basis of differential geometry, the calculation formulas for the particle time derivatives of the base vectors, metric tensor, Christoffel symbol, unit normal vector, curvature tensor and scalar curvatures on soft curved surface are derived. The limitations of particle time derivatives, e.g. the non-covariance, are pointed out. This research paves the way for studying particle time derivative of any tensor field on soft curved surface.
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OpenAlex topics: Electrowetting and Microfluidic Technologies · Surface Modification and Superhydrophobicity · Interactive and Immersive Displays
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